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No Biconditional?

  • To: mathgroup at
  • Subject: [mg61945] No Biconditional?
  • From: "Steven T. Hatton" <hattons at>
  • Date: Sat, 5 Nov 2005 01:52:47 -0500 (EST)
  • Sender: owner-wri-mathgroup at

I guess, technically, Equal will provide all the functionality that a
biconditional operator would provide.  I'm a bit surprised that, so far as
I can see, there is no biconditional in a form typically used in symbolic
logic.  I will grant that the traditional symbols are problematic in more
ways than one.  For example, <=> is sometimes used to denote definition,
and <-> is used to denote a biconditional relation.  In the contexts where
<-> is used, -> would be used as a conditional.  Unfortunately for purists
of symbolic logic, -> has been dedicated to other purposes in Mathematica. 
Is there any convention for denoting a biconditional relation in the
context of electronic documents?  That is, in the sense of symbolic logic.  

I see the <-> is available, as is <=>, but, if my observations are correct
<=> has the wrong precedence. For example in
(P \[And] Q) \[DoubleLeftRightArrow] \[Not] P \[Or] \[Not] Q,
\[DoubleLeftRightArrow] binds more tightly than \[Or] resulting in:
Or[Not[DoubleLeftRightArrow[And[P, Q], Not[P]]], Not[Q]].  There appears to
be a way to change the precedence of operators, but I don't know how to
determine what precedence I should give an operator whose behavior I
define.  Should I simply use == and suffer the indignation?
"Philosophy is written in this grand book, The Universe. ... But the book
cannot be understood unless one first learns to comprehend the language...
in which it is written. It is written in the language of mathematics, ...;
without which wanders about in a dark labyrinth."   The Lion of Gaul

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